Epidemic drinking model: a dynamical analysis employing the Mittag-Leffler kernel (Journal of Mathematical Modeling and Fractional Calculus, 2024)
One of the most helpful operators for using fractional differential equations to explain non local behaviors is the fractal fractional with Mittage-Leffler kernel fractional derivative. We proposed the fractal fractional Mittage-Leffler kernel for the drinking epidemic which is the world wide largest issue now a days. Qualitative and quantitative analysis for model and scheme are analyzed for drinking system in community. Additionally, using several well-known theorems from fixed point theory, we confirm the existence, uniqueness, analysis, and Ulam-Hyres stability of solutions to a specific class of fractional operators. Connect the drinking fractional system to a recently proposed bivariate Mittag Leffler function to solve it. Some important properties were also verified for Mittage-Leffler fractional derivative on the fractional drinking system. Comparison has been made to the integer order derivative to verify the efficiency of results and effect of drinkers in community.
Keywords: Drinking Model; Fixed Point Theorems; Ulam-Hyres Stability; Mittag-Leffler kernel